This text corresponds to a graduate mathematics course taught at Carnegie Mellon University in the spring of 1999. Included are comments added to the lecture notes, a bibliography containing 23 items, and brief biographical information for all scientists mentioned in the text, thus showing that the creation of scientific knowledge is an international enterprise.
About the Author: Luc Tartar studied at Ecole Polytechnique in Paris, France, 1965-1967, where he was taught by Laurent Schwartz and Jacques-Louis Lions in mathematics, and by Jean Mandel in continuum mechanics.
He did research at Centre National de la Recherche Scientifique, Paris, France, 1968-1971, working under the direction of Jacques-Louis Lions for his thèse d'état, 1971.
He taught at Université Paris IX-Dauphine, Paris, France, 1971-1974, at University of Wisconsin, Madison, WI, 1974-1975, at Université de Paris-Sud, Orsay, France, 1975-1982.
He did research at Commissariat à l'Energie Atomique, Limeil, France, 1982-1987.
In 1987, he was elected Correspondant de l'Académie des Sciences, Paris, in the section Mécanique.
Since 1987 he has been teaching at Carnegie Mellon University, Pittsburgh, PA, where he has been University Professor of Mathematics since 1994.
Partly in collaboration with François Murat, he has specialized in the development of new mathematical tools for solving the partial differential equations of continuum mechanics (homogenization, compensated compactness, H-measures), pioneering the study of microstructures compatible with the partial differential equations describing the physical balance laws, and the constitutive relations.
He likes to point out the defects of many of the models which are used, as a natural way to achieve the goal of improving our understanding of mathematics and of continuum mechanics.
